Details

sample43.2s

Algorithm

intervals

Results

42.9s	3342×	body	10240	exit
76.0ms	3599×	pre	80	true
34.0ms	1×	body	5120	valid
23.0ms	242×	body	80	valid
13.0ms	7×	body	1280	valid
2.0ms	3×	body	640	valid
1.0ms	4×	body	160	valid

simplify24.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	25
1	147	25
2	850	25
3	5001	25

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 7.5b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ 1.0 (exp (- t))))
0.8b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
2.7b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
2.9b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

558×	`add-exp-log`
312×	`prod-exp`
264×	`pow-exp`
250×	`div-exp`
184×	`pow-to-exp`
51×	`*-un-lft-identity`
37×	`times-frac`
36×	`unpow-prod-down`
31×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`add-cbrt-cube`
10×	`distribute-lft-out`
6×	`pow1` `pow-unpow` `associate-/r/`
5×	`cbrt-undiv` `associate-/r*`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow-pow` `frac-2neg` `clear-num` `sqr-pow`

Counts

4 → 293

Calls

4 calls:

5.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
37.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

series732.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
65.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
69.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
568.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

simplify107.0ms

Algorithm

egg-herbie

Counts

305 → 305

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	993	6127
1	3350	5877
2	5002	5877

prune557.0ms

Filtered

305 candidates to 99 candidates (32.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	301	4	305
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	302	4	306

Merged error: 0.6b

Counts

306 → 4

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ 1.0 (exp (- s))))
0.0b	(/ 1.0 (+ 1.0 (exp (- t))))
0.8b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.7b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

173×	`add-exp-log`
87×	`prod-exp`
67×	`div-exp`
55×	`pow-exp`
53×	`*-un-lft-identity`
42×	`pow-to-exp`
37×	`times-frac`
31×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-cbrt-cube`
18×	`unpow-prod-down`
11×	`distribute-lft-out`
9×	`associate-/r*`
7×	`associate-/l*`
6×	`cbrt-undiv` `associate-/r/`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-unpow` `frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`pow-pow` `sqr-pow`

Counts

4 → 176

Calls

4 calls:

6.0ms	(/ 1.0 (+ 1.0 (exp (- s))))
6.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
31.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

series819.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ 1.0 (+ 1.0 (exp (- s))))
25.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
69.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
699.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

simplify100.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	871	2983
1	3666	2728
2	5002	2724

prune652.0ms

Filtered

188 candidates to 101 candidates (53.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	188	4	192

Merged error: 0.6b

Counts

192 → 4

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ 1.0 (exp (- s))))
0.1b	(* 0.020833333333333336 (pow t 3))
0.8b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.7b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (fma t 0.25 (- 0.5 (* 0.020833333333333336 (pow t 3))))) c_n)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

176×	`add-exp-log`
90×	`prod-exp`
66×	`div-exp`
56×	`pow-exp`
43×	`pow-to-exp`
40×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`times-frac`
22×	`unpow-prod-down`
20×	`add-cbrt-cube`
12×	`associate-r`
7×	`distribute-lft-out`
5×	`pow1` `cbrt-undiv` `associate-/r*` `cbrt-unprod`
4×	`expm1-log1p-u` `cube-prod` `associate-/r/` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
3×	`pow-unpow` `associate-l` `div-inv` `sqr-pow`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`cube-mult` `pow-pow` `unpow3` `*-commutative`

Counts

4 → 174

Calls

4 calls:

5.0ms	(/ 1.0 (+ 1.0 (exp (- s))))
6.0ms	(* 0.020833333333333336 (pow t 3))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
25.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (fma t 0.25 (- 0.5 (* 0.020833333333333336 (pow t 3))))) c_n)))

series912.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ 1.0 (+ 1.0 (exp (- s))))
33.0ms	(* 0.020833333333333336 (pow t 3))
70.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
783.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (fma t 0.25 (- 0.5 (* 0.020833333333333336 (pow t 3))))) c_n)))

simplify107.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	867	2836
1	3899	2585
2	5003	2585

prune662.0ms

Filtered

186 candidates to 94 candidates (50.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	186	4	190

Merged error: 0.6b

Counts

190 → 4

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b	(* 0.5 (* s c_n))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

6×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
1×	`expm1-log1p-u` `associate-r` `*-commutative` `log1p-expm1-u` `add-log-exp`

Counts

1 → 20

Calls

1 calls:

5.0ms

(* 0.5 (* s c_n))

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

(* 0.5 (* s c_n))

simplify74.0ms

Algorithm

egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	88	77
1	320	62
2	1234	62
3	3438	62
4	5002	62

prune40.0ms

Filtered

23 candidates to 13 candidates (56.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	23	4	27

Merged error: 0.6b

Counts

27 → 4

regimes357.0ms

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	31
1	51	31

end0.0ms

sample2.7m

Algorithm

intervals

Results

2.7m	13408×	body	10240	exit
273.0ms	14456×	pre	80	true
88.0ms	1011×	body	80	valid
55.0ms	3×	body	5120	valid
19.0ms	11×	body	1280	valid
5.0ms	2×	body	2560	valid
4.0ms	5×	body	640	valid
3.0ms	13×	body	160	valid
1.0ms	3×	body	320	valid